Continuous multi-life annuities

Computes continuous joint-life, last-survivor, and reversionary whole-life annuities for two independent lives.

Usage

abarxy(x, y, i, tbl = NULL, model = NULL, ...)

abarxybar(x, y, i, tbl = NULL, model = NULL, ...)

abarx_y(x, y, i, tbl = NULL, model = NULL, ...)

abary_x(x, y, i, tbl = NULL, model = NULL, ...)

Arguments

x

Age of the first life. May be scalar or vector.

y

Age of the second life. May be scalar or vector.

i

Effective annual interest rate. May be scalar or vector.

tbl

Optional life table object retained for backward compatibility. Continuous calculations currently require model.

model

Parametric survival model.

...

Additional parameters passed to the survival functions.

Value

A numeric vector of actuarial present values.

Details

abarxy() computes the joint-life annuity.

abarxybar() computes the last-survivor annuity.

abarx_y() computes the reversionary annuity payable to the second life after the death of the first.

abary_x() computes the reversionary annuity payable to the first life after the death of the second.

These functions require a parametric survival model.

Under independence, abarxy() represents the continuous joint-life annuity, payable while both lives survive.

The last-survivor annuity satisfies $$\bar{a}_{\overline{xy}} = \bar{a}_x + \bar{a}_y - \bar{a}_{xy}.$$

The reversionary annuities are obtained as the difference between the corresponding single-life annuity and the joint-life annuity.

Examples

abarxy(
  x = 40,
  y = 50,
  i = 0.05,
  model = "uniform",
  omega = 100
)
#> [1] 10.45444

abarxybar(
  x = 40,
  y = 50,
  i = 0.05,
  model = "uniform",
  omega = 100
)
#> [1] 16.24185